Open Access Open Access  Restricted Access Subscription or Fee Access

The Persistence of Vortex Structures Between Rotating Cylinders in the 106 Taylor Number Range

David S. Adebayo(1), Aldo Rona(2*)

(1) Department of Engineering, University of Leicester, United Kingdom
(2) Department of Engineering, University of Leicester, United Kingdom
(*) Corresponding author



The flow in the annular gap d = Ro - Ri between a stationary outer cylinder of radius Ro and a co-axial rotating inner cylinder of radius Ri is characterised at large gap, over the radius ratio (η) range 0.44 ≤ η ≤ 0.53 and aspect ratio (Γ) range 7.81 ≤ Γ ≤ 11.36. These configurations are more representative of turbomachinery bearing chambers and large rotating machinery than the journal bearing geometries of narrow gap commonly reported in the literature. Particle Image Velocimetry measurements are taken across the full meridional plane over the Taylor number (Ta) range 258 × 103 ≤ Ta ≤ 10.93 × 106, which is 1000 times higher than the critical Taylor number for the onset of the first axisymmetric Taylor instability. Well-defined azimuthal vortex structures persist over this high Taylor number range, characterised by a constant number of vortices at a given aspect ratio, vortex core axial and radial motion over time, and mixing between neighbour vortices. This regime, with wavy Taylor vortex flow like features, is defined over the range 1.18 × 106 ≤ Ta ≤ 6.47 × 106. These results form a body of experimental evidence from which further progress in the understanding of the wavy Taylor vortex dynamics can be sought, through advanced flow dynamic models that reproduce the persistence of the observed flow features.
Copyright © 2015 The Authors - Published by Praise Worthy Prize under the CC BY-NC-ND license.


Particle Image Velocimetry; Concentric Cylinders; Wide Gap; Taylor Vortices; Meridional Plane PIV; High Taylor Number Flow

Full Text:



Hassan, H.Z., Gobran, M.H., Abd El-Azim, A., Simulation of a transonic axial flow fan of a high bypass ratio turbofan engine during flight conditions, (2014) International Review of Aerospace Engineering, 7 (1), pp. 17-24.

M. A. Aziz, Farouk M. Owis, M. M. Abdelrahman, Preliminary Design of a Transonic Fan for Low By-Pass Turbofan Engine, (2013) International Review of Aerospace Engineering (IREASE), 6 (2), pp. 114-127.

A. Mallock, Determination of the viscosity of water, Proceedings of the Royal Society of London 45 (1888), 126-132.

M. Couette, Études sur le frottement des liquides, Ann. Chim. Phys. 6 (1890), 433-510.

G. I. Taylor, Stability of a viscous liquid contained between two rotating cylinders, Philos. Trans. R. Soc. London A223 (1923), 289-343.

A. H. Nissan et al, The onset of different modes of instability for flow between rotating cylinders, Al. Ch. E. J. 9 (1963), 620-624.

K. W. Schwarz et al, Modes of instability in spiral flow between rotating cylinders, Journal of Fluid Mechanics 20 (1964), 281-289.

D. Coles, Transition in circular Couette flow, Journal of Fluid Mechanics 21 (1965), 385-425.

H. A. Snyder, Waveforms in rotating Couette flow, International Journal of Non-linear Mechanics 21 (1970), 659-685.

P. J. Gollub and H. L. Swinney, Onset of turbulence in rotating fluid, Physical Review Letters 35 (1975), 927-930.

P. R. Fenstermacher et al, Dynamical instabilities and the transition to chaotic Taylor vortex flow, Journal of Fluid Mechanics 94 (1979), 103-129.

R. W. Walden and R. J. Donnelly, Reemergent order of chaotic circular Couette flow, Physical Review Letters 42 (1979), 301-304.

C. D. Andereck et al, Flow regimes in a circular Couette system with independently rotating cylinders, Journal of Fluid Mechanics 164 (1986), 155-183.

R. Tagg, The Couette-Taylor problem, Nonlinear Science Today 4 (1994), 1-25.

J. M. Nouri and J. H. Whitelaw, Flow of Newtonian and non-Newtonian fluids in a concentric annulus with rotation of the inner cylinder, Journal of Fluids Engineering 116 (1994), 821-827.

A. Racina et al, Experimental investigation of flow and mixing in Taylor-Couette reactor using PIV and LIF methods, International Journal of Dynamics Fluids 1 (2005), 37-55.

S. S. Deshmukh et al, Computational flow modeling and visualization in the annular region of annular centrifugal extractor, Industrial and Engineering Chemical Research 46 (2007), 8343-8354.

S. S. Deshmukh et al, Flow visualization and three-dimensional CFD simulation of the annular region of an annular centrifugal extractor, Industrial and Engineering Chemical Research 47 (2008), 3677-3686.

H. L. Swinney and J. P Gollub, Hydrodynamic instabilities and the transition to turbulence, second ed. (Springer-Verlag, New York, 1981, pp. 139-180).

N. P. Cheremisinoff, Encyclopedia of Fluid Mechanics, (Gulf Publishing Company, Houston, 1985, pp. 237–273).

E. L. Koschmieder, Benard cells and Taylor vortices, first ed. (Cambridge University Press, Cambridge, 1993).

M. Raffel, Particle Image Velocimetry - A practical guide, second ed. (Springer, Berlin, 2007).

F. Wendt, Ingenieur-Archiv 4 (1933), 577.

D. P. Lathrop et al, Transition to shear-driven turbulence in Couette-Taylor flow, Physical Review A 46 (1992), 6390-6405.

B. Dubulle, Momentum transport and torque scaling in Taylor-Couette flow from analogy with turbulent convection, European Physical Journal B 21 (2001), 295.

A. K. Prasad, Particle image velocimetry, Curr. Sci. 79 (2000), 51-60.

P. H. Roberts, The solution of the characteristic value problem, Proceedings of the Royal Society of London A283 (1965), 550-556.

J. E. Burkhalter and E. L. Koschmieder, Steady supercritical Taylor vortex flow, Journal of Fluid Mechanics 58 (1973), 547-560.

G. P. Smith and A. A. Townsend, Turbulent Couette flow between concentric cylinders at large Taylor numbers, Journal of Fluid Mechanics 123 (1982), 187-217.

A. Recktenwald et al, Taylor vortex formation in axial through-flow: Linear and weakly nonlinear analysis, Physical Review E 48 (1993), 4444 - 4454.

B. Haut et al, Hydrodynamics and mass transfer in a Couette-Taylor bioreactor for the culture of animal cells, Chemical Engineering Science 58 (2003), 774 -784.

Y. Takeda, Quasi-periodic state and transition to turbulence in a rotating Couette system, Journal of Fluid Mechanics 389 (1999), 81-99.

G. S. Lewis and H. L. Swinney, Velocity structure functions, scaling, and transitions in high-Reynolds number Couette-Taylor flow, Physical Review E 59 (1999), 5457-5467.

L. Wang et al, Reappearance of azimuthal waves in turbulent Taylor-Couette flow at large aspect ratio, Chemical Engineering Science 60 (2005), 5555-5568.

S. T. Wereley and R. M. Lueptow, Spatio-temporal character of non-wavy and wavy Taylor-Couette flow, Journal of Fluid Mechanics 364 (1998), 59-80.

P. S. Marcus, Simulation of Taylor-Couette flow. Part 2. Numerical results for wavy vortex flow with one travelling wave, Journal of Fluid Mechanics 146 (1984), 65-113.

C. A. Jones, The transition to wavy Taylor vortices, Journal of Fluid Mechanics 157 (1985), 135-162.

K. T. Coughlin and P. S. Marcus, Modulated waves in Taylor-Couette flow Part 2. Numerical simulation, Journal of Fluid Mechanics 234 (1992), 19-46.

H. Vollmers, Detection of vortices and quantitative evaluation of their main parameters from experimental velocity data, Measurement Science and Technology 12 (2001), 1199-1207.

D. S. Adebayo, Annular flows and their interaction with a cylindrical probe, Ph.D. dissertation, Dept. Eng., University of Leicester, Leicester, UK, 2012.


  • There are currently no refbacks.

Please send any question about this web site to
Copyright © 2005-2020 Praise Worthy Prize